Finite Amplitude Compression Waves in a Collision Free Plasma
Finite Amplitude Compression Waves in a Collision Free Plasma
K W Morton
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For an initially cold plasma, then, these results depend on three parameters as shown in Figure 10: the initial field orientation 9, the mass ratio e, and the Alfven Mach number M, (or the final strength of the imposed field). In the two limits (i) 9 = 7r/2, 2(1 + sin 0), i. E. After breaking occurs. Then the time dependent solution rapidly converges to this as was shown in the earlier paper [26] on the transverse case. Even for smaller Mach numbers the time dependent solutions can be quite ac...curately predicted; the amplitude of the wave front and the oscillations behind it can be obtained from the soli- tary wave solution (3-29); and the period of the oscillations is given to within about 25^ by the linear analysis at the fast shock singularity (3-28). In particular, to lowest order in 2 2 2 m = M. - 1, the peak magnetic field is B^ = sin + m cosec 9 and the period 27r/m. But note that these oscillations do not strictly correspond to any steady flow oscillations for the entropy is still zero in these cases.
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